In this paper, we consider the scalar singlet \(H\)  at EW scale and \(Z^{\prime }\)  at TeV scale. Hence, the contributions to DM relic density from \(Z^{\prime }\) -portal are suppressed by the heavy \(Z^{\prime }\)  mass. The micrOMEGAs package [1]} is employed for the calculation of DM relic density and DM-nucleon scattering cross section. The numerical results for relic density are depicted in Fig. REF . It is clear that the SM Higgs-portal can not lead to correct relic density for both \(\sin \alpha =0.1\)  and \(\sin \alpha =0.02\) . While resonance condition \(M_{N_1}\sim M_{H}/2\)  is always required to generate correct relic density for \(H\) -portal.
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